I've had it REALLY lucky where I am (UK) because I started of with the Zelda panel and my brother with Kirby (2 different puzzles in 5 minutes!). Next time I'm at school though a friend of mine says we should streetpass so when we do he has the Pikmin puzzle (3 Puzzles in a few days!). Brilliant and complete proof there is no "State puzzle".

Did you ask them what they put down for their region when they set up the system? I haven't heard of anyone in North America getting different starting puzzles using the same state or province, and people have specifically reformatted their systems to select a different state to get a specific puzzle. Does the UK even have enough regions for the 7 puzzles — maybe that's why they give them at random instead?